Trajectory of a projectile
From Biocrawler, the free encyclopedia.
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Angle of Reach
The "Angle of Reach" (Not quite a scientific term) is the angle at which a projectile must be at in order to go a distance (d), given the velocity (v) and distance (d) itself.
sin(2θ) = 9.8d/v²
Time of Flight
The Time of Flight is the time it takes for the projectile to finish its trajectory.
t = d/[v·cos(θ)]
Maximum Distance
The Maximum Distance (D) is the distance the projectile can go at a velocity (v) at 45º
D = v²/9.8
Height at x
The "Height at x" is self-explanatory, the height of the projectile (y) at distance (x) including the initial height (i)
y = tan(θ)x - 9.8x²/{2[v·cos(θ)]} + i
Velocity at x
The Velocity at x is the current velocity (s) given x, θ, and initial velocity (v)
s² = [v·sin(θ)]² - 19.6[tan(θ)x - 9.8x²/{2[v·cos(θ)]}] = [v·sin(θ)]² - 19.6y
Distance Traveled
The Distance traveled by a projectile given initial angle and velocity is represented by D
D = [v²·sin(2&952;)]/9.8
Plotting the Motion of a Projectile
By using Height at x, x, and z-deviation (the tangent of the angle of deviation from the direction the launcher is facing, multiplied by x), you can plot the trajectory of the projectile in three dimensions.
